http://www.wiwi.uni-konstanz.de/econdoc/working-paper-series/

Un ive rs i ty o f K on s ta n z De pa rtmen t o f Econ om ics

Path Dependence and Induced Innovation

Karsten Wasiluk

Working Paper Series 2015-22

Path Dependence and Induced Innovation

Karsten Wasiluk∗

April 2015

Abstract

This paper presents an endogenous growth model that captures the origins of path depen-

dence and technological lock-in and introduces a mechanism of induced innovation, which

can trigger new research. Imperfect spillovers of secondary development can make the de-

velopment of new technologies unattractive until research ceases in the long run. Changes

in the relative supply of primary factors act as a stimulus for research as new technologies

are better suited for the new environment. A simulation using changes of crude oil prices in

the US shows the quantitative significance of the model’s implications. The model is able to

explain long waves of economic development where growth cycles are triggered by changes

in the relative factor supply. It also provides a new rationale for governmental regulations

such as Pigouvian taxes and pollution permits as they can stimulate innovation and provide

the base for the development of “green” technologies.

JEL Classification: O30, O31, O33, O44

Keywords: Path Dependence, Induced Innovation, Directed Technological Change, Growth

Cycles

∗Correspondence: Department of Economics, University of Konstanz

Email: karsten.wasiluk@uni-konstanz.de, Web: www.sites.google.com/site/karstenwasiluk

I would like to thank my supervisors Leo Kaas and Matthias Hertweck, the members of the Seminar in

Macroeconomics at the University of Konstanz, the participants of the Doctoral Workshop on Dynamic

Macroeconomics in Strasbourg (June 2010), especially Timothy J. Kehoe, for helpful comments.

1 Introduction

In this paper, I develop a model of path dependence, where the establishment of a dominant

technology leads to a technological lock-in, and propose a mechanism of induced innovation,

by which changes in the relative factor supply stimulate new research and allow to replace the

dominant technology.

Path dependence denotes the fact that the trajectory of technological development depends on

previous decisions and outcomes. The worldwide dominance of the light-water nuclear reactor

despite the fact that it is considered inferior to other reactor types, is an example for this

phenomenon. The success of the light-water reactor originates from the strong research founded

by the US navy, who needed a small reactor as energy source for its submarines. This gave

this reactor type a headstart over competing designs, so that it also became the dominant

technology for stationary nuclear power plants (Cowan, 1990). Another prominent example is

the QWERTY keyboard, which became an industry standard upon introduction with the first

typewriters and could not be replaced by better keyboard layouts because typists had been

trained for it already (David, 1985).

Path dependence can result from a number of origins. In his seminal article, Arthur (1989) points

out the existence of specific human capital, that cannot be used for the competing technologies,

network effects and technical interrelatedness, as well as increasing returns that hinder new

technologies from overcoming the existing technology. Farrell and Saloner (1985, 1986) add the

existence of standards and a large installed base as factors supporting the establishment of a

dominant technology. Also headstart advantages and setup costs may prohibit the development

of new technologies that may have a higher potential but are less productive in the short run.

Nevertheless, such a technological lock-in does not have to persist forever. Changes in the en-

vironment may provide enough incentives to overcome the dominant technology and to develop

alternatives. This notion has been proposed already by Hicks (1932), who postulated that

“A change in relative prices of factors of production is itself a spur to invention, and to invention

of a particular kind - directed towards economizing the use of a factor which has become relatively

expensive.”

The second part of this statement has found enormous attention by the literature on directed

technical change during the last years, for example in Acemoglu (1998, 2002, 2007), Kiley (1999),

and Jones (2005).1 Although this paper is related to that literature, the focus here lies on the

first part of Hicks’ statement. Can changes in the relative supply of factors provide an incentive

to research and lead to new innovations that replace the predominant technology?

A real world example for this idea is the automobile industry. During the course of the twen-

tieth century, the development of electrical cars has ceased and gasoline cars have become the

1While Hicks focused on the effect of price changes, the modern literature on directed technical change typicallyassumes exogenous changes in the (inelastic) relative supply of factors with relative prices being determinedendogenously in equilibrium. This paper follows this line as this allows to compare the results with the currentliterature. The common denominator with Hicks’ statement lies in the idea that a certain factor becomes relativelyabundant or scarce.

1

only widespread technology. However, in recent years the development of electrical, hydrogen

or hybrid vehicles has gained new momentum. With fossil fuels becoming scarce and expensive

in the near future and ongoing climate change debates, alternatives to gasoline have become

attractive again. At the end of the 1990s, the world’s biggest car manufacturer Toyota intro-

duced the Prius, a hybrid car that combines gasoline and electrical engines, which became a

huge success. Now in 2015, all major car manufacturers work on concepts for alternative drive

systems or have already brought the first models to the market. So, the prospective change of

the availability of natural resources has triggered new research, which will lead eventually to

the replacement of gasoline cars.

The model developed in this paper captures both the origins of path dependence that lead to

technological lock-in as well as the induced innovation, that can lift the economy out of the trap

again. The endogenous growth model is based on two sources of productivity growth: funda-

mental research and secondary development that builds on fundamental innovations. Secondary

development is linked to a particular fundamental technology and cannot be transferred to the

next fundamental innovation. With this, the expected productivity gain of a new fundamental

innovation decreases as the stock of secondary knowledge for the current fundamental technol-

ogy grows. This makes fundamental research less attractive and thus lowers the probability

for a new innovation. In the long run, this leads to a technological lock-in and fundamental

research ceases.

However, fundamental research does not only improve the productivity in general but can also

be directed to increase the relative marginal productivity of a particular input factor. With

this, fundamental researchers can react to changes in the relative factor supply and tailor a

new innovation optimally for the new resource endowment. Hence, if the relative factor supply

in the economy changes over time, the new fundamental innovation gains an advantage over

the predominant technology, which makes fundamental research attractive again, so that the

technological lock-in can be overcome.

With this result, the model is able to explain long wave patterns of economic development,

where periods of strong growth alternate with slow growth phases. Changes in the relative

supply of production factors induce new fundamental innovations, leading to a high-growth

phase, which slowly fades out until the next fundamental innovation is triggered by a change

in the resource endowment. The model can also explain technological backlashes, where factor

price changes can lead to the development of new technologies, which are replaced again by

the previous technology shortly after, when the price regime switches back to the old level.

Examples for this pattern can be found during the energy crises of the 1970s when research into

alternative energy sources and engines soared but was quickly dropped again during the oil glut

of the 1980s.

To illustrate the quantitative significance of the model’s implications, I simulate the effect of

the relative changes in the crude oil price compared to renewable energy sources in the US from

1870 onward. The simulation results indicate that fundamental research and hence productivity

growth is triggered by changes in the oil price. Due to the ongoing price changes, fundamental

research is stimulated again and again and does not die out over time. By contrast, in the

2

cross-check simulation without price changes, fundamental research and productivity growth

cease over time and the economy becomes trapped in a technological lock-in. This indicates

that the model’s implications are quantitatively relevant.

This paper adds to the literature on path dependence and technological lock-in, where agents

decide on adopting new technologies, while specific human capital or secondary development

may stop them from doing so (Arthur, 1989; Brezis et al., 1993; Chari and Hopenhayn, 1991;

Parente, 1994; Jovanovic and Nyarko, 1996). This paper is most closely related to Redding

(2002), who proposes a model of endogenous growth, in which path dependence can lead to a

technological lock-in. This model continues that work and adds a mechanism by which induced

innovation can lift the economy out of the lock-in. This allows for growth and fundamental

research in the long run, whereas in Redding’s model, there was no possibility to continue

research.

The paper is linked to the literature on directed or biased technological progress which has

its origin in the ideas of Hicks (1932) and was formally characterized initially in the works

of Fellner (1961), Kennedy (1964), Samuelson (1965), Ahmad (1966), Drandakis and Phelps

(1966), and Binswanger (1974).2 Since the seminal article by Acemoglu (2002), who proposed a

micro-founded endogenous growth model in which changes in the supply of primary factors lead

to directed technological change, this literature has attained new momentum (Acemoglu, 1998,

2007; Kiley, 1999; Jones, 2005; Wing, 2006). Recent empirical studies have found supportive

evidence for directed technological progress. Newell et al. (1999) show that the energy price

hikes due to the oil crises induced the development of more energy-efficient air-conditioners;

Popp (2002) finds that higher energy prices have significantly increased the relative amount of

energy-saving innovations in the U.S.; a similar result is obtained by Lanzi and Sue Wing (2011)

for a panel of OECD countries; and Aghion et al. (2012) demonstrate that increased fuel prices

raised the number of clean innovations in the U.S. automobile industry.

In this paper, the focus is not so much on the mechanism that determines the direction of

technological change but more on the innovation stimulus that is triggered by a change in

the relative supply of primary factors. Nevertheless, the model’s implications concerning the

bias of technological progress for relative factor supply changes are in line with the literature.

With the focus on induced innovation, this paper also contributes to the growing literature

on environmental protection and technological change (Goulder and Schneider, 1999; Unruh,

2002; Acemoglu et al., 2012a,b; Gans, 2012). In difference to those models, here, changes in

the relative supply of primary factors, which may come in the form of Pigouvian taxes on fossil

fuels or pollution permits, can induce a “green” innovation which displaces the dominant “dirty”

technology and thus increase the total innovation rate.

Finally, this paper adds to the literature on long-run patterns of economic development and

growth cycles (Kondratieff, 1984; Schumpeter, 1939; Mensch, 1979; Marchetti and Nakicenovic,

1979; Graham and Senge, 1980; Volland, 1987; Grubler and Nakicenovic, 1991). The model

proposes an analytical explanation based on the decisions of rational agents how new cycles are

2See also Acemoglu (2003) for an overview of the early literature.

3

triggered by changes in the supply of production factors, which is a stylized fact in long wave

analysis.

The paper is organized as follows: the next section introduces the model; Section 3 derives the

economy’s equilibrium and the paper’s main results; Section 4 analyzes the bias of technological

change that is induced by a change in factor supply and compares it to the results of the existing

literature; in Section 5, the effect of oil-price changes for the US economy is simulated; and

Section 6 concludes and discusses opportunities for future research.

2 The Model

General Setup

The model is set in discrete time on an infinite horizon. The economy is populated with

overlapping generations of uniform agents of mass one who live for two periods. Each agent is

endowed with one unit of labor per period. In addition, there is an exogenously given perfectly

inelastic supply of primary inputs Q and Z in every period. These primary inputs are supplied

competitively at market prices pQ, pZ and are not owned by the agents.3 Generations are indexed

by t ∈ [1,∞) and lifetime periods by 1 and 2 such that pQ2t refers to the price of input Q in the

second life period of generation t for example.

The economy comprises four sectors: Fundamental research and secondary development, which

take place during the first period of an agent’s life, and intermediate and final goods production

during period 2. Each final good producer produces an individual final good indexed by i.

These final goods are imperfect substitutes for consumption. Intermediate goods are produced

from primary inputs Q,Z and used for final goods production. Each fundamental innovation

creates a new type of intermediate good. The different types of intermediate goods that are

available are indexed by k.

Fundamental research is modeled as directed technological progress with uncertain success that

generates a sequence of blueprints for intermediate goods production technologies with increas-

ing productivity. Secondary development takes place under certainty and takes the form of

continuous productivity improvements in final goods production. Secondary development is

specific to a particular type of intermediate good, similar to Brezis et al. (1993), Jovanovic and

Nyarko (1996), and Redding (2002). This implies that for each new fundamental innovation,

which produces a new type of intermediate good, the stock of secondary knowledge has to be

accumulated again.

The total productivity of the economy in terms of transforming raw inputs into final goods is

determined by the joint productivity of intermediate and final goods production and depends

on the type of intermediate good that is used and the stock of secondary knowledge that has

been developed for this type of intermediate good. This is illustrated in Figure 1.

3These assumptions are not necessary for the results but simplify the analysis of the equilibrium.

4

Joint Productivity

Secondary Development

x1

x2

x3

x4

Fu

nd

amen

tal

Inn

ovati

on

s

Figure 1: Joint productivity of fundamental technology and secondary development

Timing of Decisions

At the beginning of period 1, newborn agents inherit the blueprints for intermediate goods

production technologies from previous generations and the body of secondary knowledge that

has been accumulated up to this time.4 The agents then decide whether to become fundamental

researchers or secondary developers. In the remainder of period 1, fundamental researchers aim

to discover a new technology for intermediate goods production while secondary developers

augment the body of secondary knowledge for a chosen type of existing intermediate good.

During this process, the latter also acquire the skills needed to become final good producers in

period 2. Consequently, the initial decision to continue along fundamental research or secondary

development marks a decision on lifetime labor supply.

At the end of period 1, all research uncertainty is revealed. If a success in fundamental research

has been made, the successful researcher becomes the monopoly supplier of the new type of

intermediate good in period 2. If no new fundamental innovation has been made, an already

existing type of intermediate good is produced competitively. Secondary developers become final

good producers under monopolistic competition; unsuccessful fundamental researchers have no

profession in the second period.

Production and Consumption

Intermediate goods production uses primary inputs Q and Z in a CES production function with

constant returns to scale,

x2t,k = Ak

[ψ

1εkQ

ε−1ε

2t + (1− ψk)1εZ

ε−1ε

2t

] εε−1

. (1)

4The inherited technologies and secondary development constitute the endogenous state variables of the econ-omy.

5

The productivity of intermediate goods production Ak and the share parameter ψk are linked to

the type of intermediate good xk. They are determined in the process of fundamental research

which is specified below. The market price of intermediate goods is denoted pxk.

Final good producers use a linear CRS production function and the intermediate good as input,

y2t,i = S2t,k x2t,k(i), (2)

where S2t,k denotes the stock of secondary knowledge for intermediate good xk that has been

accumulated. It is implicitly assumed, that all final goods producers possess the same amount

of secondary knowledge. Given that the agents inherit the body of secondary knowledge at

the beginning of period 1, this assumption states that all secondary developers are equally

productive in augmenting the stock of secondary knowledge. This assumption can be relaxed

to give y2t,i = S2t,k(i)x2t,k(i), however, this does not change the results and only complicates

the model.

All production activities take place in period 2, hence income is only generated in the second

life period of each generation. There are no credit markets, so consumption takes place only

in period 2. Agents are indexed by j; they are risk neutral and do not suffer disutility from

supplying labor. They have Dixit-Stieglitz type preferences on the basket of final goods, so the

lifetime utility of an individual agent is given by

ut,j =

(∫ Lt

0c2t,i(j)

ρ di

) 1ρ

, (3)

where c2t,i(j) denotes the agent’s consumption of final good y2t,i at price py2t,i and Lt denotes

the measure of final good producers in generation t, which gives the range of different final

goods.5 Since final goods are imperfect substitutes, 0 < ρ < 1.

Fundamental Research

Fundamental researchers try to discover a better production technology for intermediate goods.

Let xm denote the latest type of intermediate good that is available at the start of the first

period of generation t. Every researcher creates an innovation that results in a new type of

intermediate good xm+1 with probability p. The successful innovator obtains a patent for the

innovation that is valid for one period (that is until the end of the innovator’s life). Let Rt

be the mass of researchers of generation t. Since Rt consists of infinitely many elements, the

resulting aggregate innovation probability is approximated by a Poisson distribution (Feller,

1950). Hence the aggregate probability that a new innovation is made is given by

Ω(Rt) = 1− e−pRt . (4)

5Lt does not carry an index for the lifetime period since the decision for labor supply is a lifetime decisionand Lt refers to the mass of secondary developers in generation t in the first lifetime period and to final goodproducers in the second period.

6

If more than one innovation is created, the patent is attributed to one of the innovators by

lottery. The individual probability of obtaining the patent for a new technology is given by

P (Rt) =1− e−pRt

Rt. (5)

The aggregate probability to discover a new fundamental technology increases in Rt whereas

the individual probability to obtain a patent decreases in Rt.

Fundamental research can be directed so that not only general productivity is increased but also

the relative marginal product of one particular input factor. This means that researchers can

adjust the intermediate goods production technology if the relative supply of primary factors

Q,Z changes, in order to use these resources optimally.

The effect of a new fundamental innovation is composed of two parts. First, the general pro-

ductivity of intermediate goods production evolves with productivity factor A according to

Am+1 = γAm = γm+1A0 with γ > 1, (6)

where A0 is normalized to 1. Second, fundamental innovators adjust the direction of tech-

nological progress by choosing the optimal share parameter ψm+1 for the intermediate goods

production function, which changes the relative marginal productivity of the input factors.

Secondary Development

The stock of secondary knowledge for a specific intermediate good is increased by secondary de-

velopers during the first lifetime period of every generation. Secondary development is regarded

as a product of the following three processes: the accumulation of specific human capital needed

to use the respective fundamental technology efficiently, engineering refinements that make the

fundamental technology more productive, and the creation of supplementary technologies and

networks that are needed to release the productive potential of the underlying fundamental

technology. These achievements are specific for every underlying fundamental technology. So

when a new fundamental technology is discovered, secondary development starts from the be-

ginning again. These assumptions capture the essence of the origins of path dependence as

described in the introduction.6

Secondary development features diminishing marginal returns so that the marginal productivity

improvements decline with ongoing secondary development. When a new technology in form of

a fundamental innovation is introduced, final good producers have to accommodate themselves

with this technology and learn to use it efficiently. At the beginning, this will lead to great

productivity improvements but further gains in efficiency are harder to achieve. Also a new

technology is most often not perfect at the start-up but rather comes as a beta-version. So in

the early days, there are a lot of possibilities for improvements (Rosenberg, 1994). After the

6The assumption of zero spillovers of secondary development can be relaxed to allow for imperfect spilloversbetween fundamental technologies, so that a part of the accumulated stock of secondary development can be usedwith a new fundamental technology, similar to Redding (2002). This does not change the fundamental results ofthe model.

7

first important rework has been undertaken, future improvements will be of lesser importance

until finally the productive potential of the underlying technology is completely released.7

Secondary developers decide for which type of intermediate good they undertake secondary

development and spend the first period augmenting the stock of secondary knowledge for this

technology. The stock of secondary knowledge for the chosen technology xk evolves during the

agents’ first lifetime period according to

S2t,k = µSφ1t,k with: µ > 1, 0 < φ < 1, (7)

where S1t,k denotes the stock of secondary development for technology k that has been inherited

from the previous generation.

Notice, that due to diminishing returns of secondary development, the economy can exhibit

growth in the long run only by fundamental innovations. This is similar to the assumptions in

Jovanovic and Nyarko (1996).

3 Equilibrium

Given the time structure of decisions, the model is solved by backward induction for the de-

cisions of an arbitrary generation t and given number of fundamental technologies available

with corresponding body of secondary development. First, I derive the equilibrium in final

and intermediate goods markets in period 2 for a given number of fundamental researchers and

secondary developers. Two states of the world have to be considered in this analysis: successful

and unsuccessful fundamental research in period 1. After that, the equilibrium allocation of

fundamental research and secondary development in period 1 as well as the choice of a fun-

damental technology for secondary development and the direction of fundamental research is

obtained.

Period 2

The equilibrium in the final goods market is independent of success in fundamental research in

period 1. Agents optimize their consumption portfolio subject to their preferences given in (3)

and their individual budget constraint∫ Lt

0py2t,i c2t,i(j) di ≤ E2t(j), (8)

where E2t(j) denotes the agent’s income in period 2, depending on his lifetime labor decision

and research success.

This yields individual demand for each type of final good

c2t,i(j) =

(py2t,iP2t

)− 11−ρ E2t(j)

P2t, (9)

7See also the discussion in Doraszelski (2004) about different specifications for secondary development.

8

with price index

P2t =

[∫ Lt

0py

− ρ1−ρ

2t,i di

]− 1−ρρ

. (10)

Final goods producers maximize their profit, subject to demand for final goods derived above.

As in Dixit and Stiglitz (1977), the optimal competitive-monopoly price is a constant mark-up

over marginal cost MCy2t,i

py2t,i =1

ρMCy2t,i.

8 (11)

To derive the equilibrium results for intermediate goods production, the two possible cases

for the period 1 outcome, successful and unsuccessful fundamental research, are considered

separately.

Unsuccessful Fundamental Research in Period 1

If no fundamental innovation was made in period 1, all types of existing intermediate goods are

free of patent protection and can be produced by competitive enterprises. Intermediate goods

producers choose the type of intermediate good that delivers the highest joint productivity

in combination with the body of secondary knowledge in period 2 to maximize their output.

This involves a potential trade-off between productivity in intermediate goods production and

productivity in final goods production, which depends on the stock of secondary knowledge that

has been accumulated for each type of intermediate good. Let xn denote the chosen intermediate

good. The type n is defined by

S2t,nAn

[ψ

1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

] εε−1

= supk≤m

S2t,kAk

[ψ

1εk Q

ε−1ε

2t + (1− ψk)1ε Z

ε−1ε

2t

] εε−1

,

(12)

where Q2t, Z2t denote the exogenous supply of factors Q, Z during this period.

Since intermediate goods production is competitive, the price px2t,n equals marginal production

costs and intermediate goods producers make zero profits. Intermediate good xn is the only

type of intermediate good that is produced and it is taken as the economy’s numeraire, so

px2t,n = 1. (13)

8Since preferences are homothetic, the distribution of income among agents does not influence equilibriummark-ups of final good producers (Foellmi and Zweimueller, 2003).

9

Since this type of intermediate good is used by all final good producers, marginal costs are the

same for all types of final goods, hence

py2t,i = py2t =1

ρS2t,n. (14)

Total demand for Qt and Zt equals the supply Qt, Zt, hence total intermediate goods production

is given by

X2t,n = An

[ψ

1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

] εε−1

. (15)

Primary factors are paid their marginal value product

pQ2t =

∂An

[ψ

1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

] εε−1

∂Q2t, pZ2t =

∂An

[ψ

1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

] εε−1

∂Z2t,

(16)

and the individual profit of final good producers is given by

πy2t,n =1− ρρ

X2t,n

Lt(17)

Successful Fundamental Research in Period 1

If fundamental research was successful in period 1, the innovator obtains a patent for the

new intermediate good xm+1 and becomes the monopoly supplier of this intermediate good in

period 2. The monopolist maximizes his profit given the demand for intermediate goods and

takes the prices for primary inputs Q and Z as given9

maxpx2t,m+1

px2t,m+1x2t,m+1 − pZ2tZ2t − pQ2tQ2t, (18)

s.t. x2t,m+1 = Am+1

[ψ

1εm+1Q

ε−1ε

2t + (1− ψm+1)1εZ

ε−1ε

2t

] εε−1

,

px2tm+1

S2t,m+1≤ 1

S2t,n,

S2t,m+1 = 1.

Notice, that no secondary development has been undertaken yet for the new technology, there-

fore S2t,m+1 = 1. The resulting monopoly price is given by

px2t,m+1 =1

S2t,n. (19)

9Even though the monopolist is the only buyer of primary factors in equilibrium, he is in competition with in-dependent producers of intermediate goods of the next best quality n. Therefore he can not act as a monopsonisticbuyer and takes factor prices as given.

10

This price secures the monopolist the whole market for intermediate goods because the marginal

cost for final good producers are equal to the best available alternative xn. Increasing the price

would lead to zero profits because final good producers are not willing to pay a higher price

and independent intermediate goods producers, who offer intermediate goods of type xn would

fill the gap. The price for the new intermediate good is lower than for intermediate goods of

previous generations. The new intermediate good is equally productive as its predecessors but

final goods producers have not had the time yet to build up secondary knowledge for the new

type of intermediate good. Therefore, the new intermediate good is less attractive to them and

only marketable at a lower price. However, the production of the new intermediate good needs

less resources, so the monopolist is able to make a profit.

Since the marginal cost for final good producers is equal to that in the case of unsuccessful

research in period 1, the price for a final good py2t remains the same and is independent of

research success.

Equilibrium intermediate goods output is given by

X2t,m+1 = Am+1

[ψ

1εm+1Q

ε−1ε

2t + (1− ψm+1)1ε Z

ε−1ε

2t

] εε−1

, (20)

and the profit for the successful fundamental researcher is given by

πX2t,m+1 =1

S2t,nX2t,m+1 − pZ2tZ2t − pQ2tQ2t. (21)

Using the fact that pZ2tZ2t + pQ2tQ2t = X2t,n, the monopolist’s profit can be written as

πX2t,m+1 =X2t,m+1 − S2t,nX2t,n

S2t,n. (22)

This equation makes it clear that the overall productivity based on the new type of intermediate

good, even without any secondary development in the final goods sector, must be higher than

the combined productivity of the competing intermediate goods production technology together

with the respective stock of secondary knowledge. Otherwise fundamental researchers would not

make positive profits, which implies that nobody would have wanted to become a fundamental

researcher in the first period.

The final good producers’ individual profit is given by

πY2t,m+1 =1− ρρ

X2t,m+1

S2t,nLt. (23)

Period 1

At the beginning of period 1, agents decide whether to become a fundamental researcher or

to go into secondary development and become a final good producer in the second period.

Fundamental researchers then have to decide, in which direction to focus their research, while

secondary developers have to choose the type of existing intermediate good for which the stock

11

of secondary knowledge will be increased. These decisions depend on the agents’ expectations

in the first period about the endowment with primary input factors in period 2. The expected

supply of primary factors is denoted by Q2t ≡ E1t

(Q2t

)and similar for Z2t.

The optimal choice for the type of intermediate good for secondary development is very similar

to the choice of the best production technology in period 2. Secondary developers choose the

intermediate good, for which the final goods output in the next period is maximized, given the

expected factor supply in period 2 and the contribution to the secondary stock of knowledge by

the developers themselves during the first period. The chosen technology n is defined by

µSφ1t,nAn

[ψ

1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

] εε−1

= supk≤m

µSφ1t,kAk

[ψ

1εk Q

ε−1ε

2t + (1− ψk)1ε Z

ε−1ε

2t

] εε−1

.

(24)

If the relative supply of input factors is expected to remain constant, the chosen technology

for secondary development n is the same technology that is currently used by the previous

generation for production in their second lifetime period. Furthermore, if the relative factor

supply actually remains constant, than technology n is identical to technology n, which is chosen

for production in period 2.10

Fundamental researchers decide on the optimal share parameter ψm+1 that determines the rel-

ative productivity of the primary factors Q,Z with the new intermediate goods production

technology, taking the expected supply of these factors in the next period into account. Equa-

tion (22) shows that the prospective monopolist’s profit increases in the amount of intermediate

goods that can be produced with the given amount of Q2t and Z2t. Therefore, fundamen-

tal researchers choose ψ∗m+1(Q2t, Z2t) to maximize expected output from intermediate goods

production:

ψ∗m+1(Q2t, Z2t) = arg max γAm

[ψ

1εm+1Q

ε−1ε

2t + (1− ψm+1)1ε Z

ε−1ε

2t

] εε−1

. (25)

Proposition 1. For ε 6= 1, a unique interior solution for the optimal value of ψm+1 exists,

that maximizes intermediate goods production subject to the economy’s expected relative factor

supply. The optimal ψm+1 is unique for every expected relative supply of primary factors Z2t

Q2t.

Proof. For the proof, derive the first order condition for maximization of equation (25). This

gives

ψm+1 =Q2t

Q2t + Z2t

,

which proves both parts of the proposition.

10This could of course also be true if the actual relative factor supply in the second period is different buttechnology n is still the best available technology. However, this is not necessarily the case.

12

Corollary 1. If the expected relative supply of primary input factors remains constant after

a fundamental innovation, fundamental researchers of the following generations do not change

the share parameter ψ in their research.

Corollary 1 states that once the intermediate goods production technology has adjusted to a

certain relative supply of input factors, technological progress becomes factor neutral. Only if

the relative supply of input factors changes (or is expected to change), fundamental research

becomes biased and changes the relative marginal productivity of input factors.

The final step to close the model is to determine the equilibrium levels of employment in

fundamental research and secondary development. An individual fundamental researcher makes

an innovation and receives a patent with probability P (Rt). This allows him to extract profits as

the monopolistic intermediate goods producer in the second period. An unsuccessful researcher

gains zero profits. The expected lifetime income of a fundamental researcher is thus given by

V Rt =

P (Rt)

γm+1

[ψ

1εm+1Q

ε−1ε

2t + (1− ψm+1)1ε Z

ε−1ε

2t

] εε−1

− µSφ1t,nγn[ψ

1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

] εε−1

µSφ1t,n.

(26)

Final goods producers are able to extract competitive-monopoly profits irrespective of success

in fundamental research in period 1. However, successful fundamental research increases the

profits of final goods producers. So the expected lifetime profit for secondary developers is given

by

V St = Ω (Rt)

1− ρρ

γm+1

[ψ

1εm+1Q

ε−1ε

2t + (1− ψm+1)1ε Z

ε−1ε

2t

] εε−1

µSφ1t,n (1−Rt)

+(1− Ω (Rt)

)1− ρρ

γn[ψ

1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

] εε−1

1−Rt, (27)

where the fact is used that Lt = 1 − Rt. It can be seen that if the mass of fundamental

researchers nears one, the profit of secondary developers becomes infinite, hence there will be

always a positive amount of secondary developers in equilibrium. With this, the arbitrage

equation that determines the amount of fundamental and secondary researchers is given by

V Rt ≤ V S

t , (28)

13

which can be rearranged to yield

1 ≥ γm+1−n

µSφ1t,n

ψ 1εm+1Q

ε−1ε

2t + (1− ψm+1)1ε Z

ε−1ε

2t

ψ1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

εε−1

ρ− (1− ρ) Rt1−Rt

ρ+ (1− ρ)1−Ω(Rt)Ω(Rt)

Rt1−Rt

. (29)

Proposition 2. If the arbitrage equation is binding, a unique positive equilibrium level of fun-

damental researchers Rt exists.

Proof. The nominator of the RHS of (29) strictly decreases in Rt, whereas the denominator

increases in Rt. While the first part can be directly seen, showing the monotonous behavior of

the denominator demands more work. The derivative of the nominator with respect to Rt is

given by

∂(ρ+ (1− ρ) e−pRt

1−e−pRtRt

1−Rt

)∂Rt

= (1− ρ)e−pRt

(1− e−pRt − pRt(1−Rt)

)(1− e−pRt)2 (1−Rt)2

. (30)

Equation (30) is non-negative iff:

1− e−pRt − pRt(1−Rt) ≥ 0. (31)

The left side of above expression is strictly convex and the global minimum of the function is at

Rt = 0. Plugging this result back into (31) validates the fact that the nominator of the arbitrage

equation increases in Rt. Hence the RHS of the arbitrage equation is strictly decreasing in the

number of fundamental researchers, whereas the LHS is constant, so a unique equilibrium exists

if the arbitrage condition is fulfilled.

If the arbitrage equation is not binding, the expected lifetime income of fundamental research

is always lower than that of secondary development and there is no fundamental research in

equilibrium.

Proposition 3. Equilibrium employment in fundamental research is monotonically decreasing

in the stock of accumulated secondary knowledge S1t,n for the best existing type of intermediate

good xn. Further, a critical value for the stock of accumulated secondary knowledge S∗1t,n > 1

exists at which equilibrium employment in fundamental research becomes zero and technological

lock-in occurs.

Proof. The RHS of the arbitrage equation is decreasing in S1t,n and decreasing in Rt, so the

number of fundamental researchers decreases as S1t,n increases. The second part follows directly.

Proposition 2 captures the essence of the problem of path dependence. The more secondary

investment has been put into an existing technology, the more difficult it becomes for a new

technology to outperform its predecessor. This makes searching for new technologies less attrac-

14

tive, since the profit that can be earned decreases. The negative effect of the existing stock of

secondary development on the equilibrium level of fundamental research is depicted in Figure 2.

In this model, two competing forces that determine the profitability of a fundamental innovation

exist. On the one hand, each new type of intermediate good yields a productivity gain in

intermediate goods production. On the other hand, there is a loss of productivity in final

goods production, that comes from loosing the stock of secondary knowledge when production

switches to the new type of intermediate good. As long as the first effect is stronger, a new

type of intermediate good yields an overall improvement in productivity, from which profits

for the successful fundamental innovator can be extracted. However, the larger the stock of

secondary knowledge that benefits the existing rival intermediate good grows, the lower the

productivity gain from using a new intermediate good becomes. Consequently, the potential

monopoly profit for fundamental researchers decreases. Therefore, fewer agents are willing to

undertake fundamental research while a greater number prefers to work as secondary developers.

This process aggravates until no agent finds it attractive any more to engage in fundamental

research.

This results in a technological lock-in in which no fundamental research is conducted and no

new types of intermediate goods are produced. With the assumptions on the evolution of the

productivity of intermediate goods production by fundamental research (6) and the improve-

ments of final goods production by secondary development (7), it becomes clear that unlimited

growth is only possible through fundamental innovations. Secondary development gradually

releases the underlying productive potential of the associated intermediate good. Once this

potential is completely exhausted, there is no further room for improvement. Therefore, the

economy cannot grow endlessly through secondary improvements alone. Once the economy has

been trapped in a technological lock-in, economic growth will quickly cease.

S1t,n

Rt

Lock-in

S∗1t,n

Figure 2: Equilibrium number of fundamental researcherswith respect to accumulated secondary development

The process of becoming trapped in an equilibrium with no fundamental research is self-reinforc-

ing. Every period without success in fundamental research, the stock of secondary knowledge

for the competing intermediate good increases. This makes fundamental research less attractive

for workers of the next generation, resulting in a smaller number of fundamental researchers.

Consequently, the probability to make a new fundamental innovation in the next period is

15

lowered. So with every period without fundamental research success, the probability to end

up in a no-growth equilibrium increases. Fewer and fewer workers find it attractive to become

fundamental researchers until fundamental research ceases completely.

Proposition 4. Let ε 6= 1, then a change in the expected relative supply of primary factors Q2t

Z2t

compared to the situation when the production technology for the competing type of intermediate

good xn was developed, increases the equilibrium number of workers in fundamental research.

Proof. By Proposition 1, for every expected relative supply with primary factors Q2t

Z2t, a unique

optimal ψ∗ exists. Therefore, if the expected relative resource endowment has changed since the

competing type of intermediate good xn was developed, fundamental researchers will change

the share parameter so that ψm+1 6= ψn. Furthermore, since ψm+1 is chosen to be the optimal

ψ∗ for the expected relative endowment Q2t

Z2t, it is true that

ψ 1εm+1Q

ε−1ε

2t + (1− ψm+1)1ε Z

ε−1ε

2t

ψ1εn Q

ε−1ε

2t + (1− ψn)1ε Z

ε−1ε

2t

εε−1

> 1.

This implies that the right hand side of the arbitrage equation (29) increases when the expected

relative supply of primary factors in the economy changes. Since the right hand side of the

arbitrage equation decreases in the number of fundamental researchers, a change in the relative

endowment with primary factors results in a higher number of fundamental researchers.

Corollary 2. If the change in the expected relative supply of primary factors is large enough,

fundamental research Rt is positive.

Proposition 4 captures the original idea of induced innovation. Just as in Hicks (1932), it

states that a change in the availability of factors of production stimulates innovation. The

intuition behind Proposition 4 is as follows. A new fundamental innovation has to compete

against previous types of intermediate goods which have already benefited from secondary

development, however, it has the advantage that it can be adapted to a change in relative

factor supply. Hence, if the relative supply of primary factors changes, the productivity gain

of the new fundamental innovation becomes larger. The opportunity to adjust the direction of

technological change makes the new fundamental innovation more profitable and thus provides

an incentive for workers to go into fundamental research. This effect becomes stronger, the

stronger the change in the relative factor supply is.

If the economy has been trapped in a technological lock-in, a change in the relative supply of

primary factors can make fundamental research attractive again, which is captured by Corollary

2. With the possibility to adapt the new fundamental technology to the change in relative

factor supply, the new innovation now outperforms the legacy technology which was created

for a different resource regime. The probability to escape a lock-in increases, the stronger the

change in the relative supply of primary factors is. Notice, that a great change in the relative

endowment does not have to come within one period but the relative supply may change in little

steps. As long as the incentive effect is not strong enough, fundamental research does not start.

16

However, once the difference between the actual relative factor supply and the endowment for

which the competing technology had been developed has become large enough, fundamental

research becomes attractive again and starts anew.

If the relative factor supply has enough variation over time, the model is able to generate tech-

nological progress and economic growth in the long run. During periods with little variation in

the supply of primary factors, employment in fundamental research may go down until funda-

mental research stops and technological progress eventually ceases. However, if at some point

in time substantial shifts in the relative factor supply occur, or if over time small changes accu-

mulate to larger ones, the economy is lifted out of the lock-in and fundamental research starts

again. The result is permanent growth that fluctuates between periods with more fundamental

research and periods with little or no fundamental research.

The positive effect of a change in the relative supply of primary factors on fundamental research

is illustrated in Figure 3. Similar to Figure 2, it shows the amount of fundamental research as

a function of the stock of secondary development that has been accumulated for the competing

technology. The solid line depicts the basic scenario with no changes in the relative factor supply

where fundamental research ceases for a high level of secondary development. The dashed line

in contrast displays the amount of fundamental research when the relative factor supply has

changed by 25%.11 It can be seen that the amount of fundamental research increases for all

levels of secondary development. With this, secondary development has to be higher before

fundamental research ceases. The dash-dotted line shows the results for a change in the relative

factor supply by 50%. It turns out, that the increase in fundamental research is much higher

now, so the positive effect of induced innovation grows progressively as the relative factor supply

changes.

S1t,n

Rt

Q2t

Z2t= 1

Q2t

Z2t= 1.25

Q2t

Z2t= 1.5

Figure 3: Effect of changes in relative factor supply on fundamental research

An important implication of the model is that governmental regulations, that affect the availabil-

ity of primary factors, can act as a stimulus to innovative activity and induce new innovations.

This becomes especially relevant in the context of environmental protection. A growing lit-

erature discusses the possibilities and limitations of bringing the economy on a clean growth

track that avoids the growth of greenhouse gas emissions and the depletion of natural resources

11The direction of the change does not play a role.

17

(Goulder and Schneider, 1999; Unruh, 2002; Acemoglu et al., 2012a,b; Gans, 2012). This model

predicts, that regulations reducing the availability of the factor which is harmful to the envi-

ronment, for example a limitation of pollution permits or Pigouvian taxes on fossil fuels, induce

the development of technologies that use the now scarce factor less.

Unlike other models such as Acemoglu et al. (2012a,b), the process of switching to a new

technology with a different input factor utilization does not take place gradually but rather

comes as one fundamental new innovation like the change from gasoline cars to electrical vehicles

or from fossil-fuel based electricity generation to solar energy. However, this implies also that

the push from governmental regulation (or natural changes in the relative supply) must be

strong enough to overcome the technological lock-in. Hence small regulations may have no

effect as they are not sufficient to induce a replacement of the dominant technology. This could

lead to the wrong conclusion that this kind of policy is not able to put the economy on a clean

growth track, however, the truth is that the policy has to be intensified to increase the changes

in the relative factor supply and induce the switch to a clean technology.

The model is also able to provide an explanation for the long wave patterns of economic devel-

opment, also known as Kondratiev waves, during which periods with rapid growth are followed

by periods with little or no growth. In this model, a new fundamental innovation produces dras-

tic technological progress followed by a high-growth phase with strong secondary development,

which yields the upswing phase of the cycle. Then in the downswing phase, secondary im-

provements slowly fade out until the next fundamental innovation arrives. Many authors point

out that the turning points of these movements are marked by strong changes in the price of

commodities; especially the scarcity or price peak of the current dominant energy source marks

the begin of a new cycle (Graham and Senge, 1980; Marchetti and Nakicenovic, 1979; Volland,

1987; Grubler and Nakicenovic, 1991). In the model presented here, these price changes lead

to increased fundamental research, which can trigger a new fundamental innovation and thus

start a new growth cycle. So the model is able to replicate this stylized fact.

An example for the start of such a long economic cycle is the process in the eighteenth century

leading to the Industrial Revolution in England. As Acemoglu (2002) points out, the great

increase in skill-replacing technologies which took place in England at that time, coincided

with the sudden increase in the supply of unskilled workers due to migration and other effects.

Acemoglu concludes, that this increase was the source for the bias of technological progress

towards unskilled workers at this time. This paper follows this conclusion,12 but goes one step

further by arguing that the sudden increase in the availability of unskilled labor was also the

very source of the rapid technological progress itself. The shift in the supply of unskilled workers

provided the necessary incentive to introduce new technologies of cheap mass production that

made use of these unskilled workers, compared to the previously dominating artisan production

that required specialized craftsmen.

An interesting feature of the model is, that it can explain technological backlashes where a new

technology is developed but is given up after a short time and replaced again by the previous

12See also the next section on the direction of technical progress in the model compared to the results inAcemoglu (2002, 2007).

18

technology. This happens if a change in the supply of input factors is only a temporary shock.

During the shock, new technologies are developed which are designed for the changed factor

supply. Once the supply returns to the old state, legacy technologies that were designed for that

factor supply become suddenly more profitable again than the newer interim technology. The

big shocks to worldwide oil supplies during the oil crises in the 1970s provide an example for

this switch-back effect. During that time, research in alternative energies and on economizing

energy increased tremendously. In 1973, Europe’s greatest research center for solar energy was

founded in Almeria in Spain. Around the same time, a number of solar power plants were

built in California and other parts of the US. However, as the oil price returned to a normal

level after 1980, research in this direction was quickly given up and the few research solar power

stations remained the only ones. So the newly developed technologies remained unused for mass

commercial energy production. That is true until the late 1990s, when increasing energy prices

and the public debate about climate change triggered research in this direction again.

In the extreme case, a new technology is developed with a certain (expected) factor endowment

in mind in the first period. However, if the relative factor supply returns to old levels in

the second period, the new technology might not be used at all, even though it appeared to

be profitable during the first period. The history of hybrid automobiles brings this to the

point. The first gasoline-electric hybrid automobile was invented already in 1901 by Ferdinand

Porsche, but, although technologically outstanding, could not gain a relevant market share and

hybrid automobiles were not further developed. Then during the oil crises in the 1970s, US

manufacturer Briggs & Stratton developed a hybrid car that arrived at the market in 1980.

However, since energy prices had declined again already, the concept remained unsuccessful.

So even though the new technology seemed to be profitable during development, its time was

over before it could reach the market. Only at the end of the 20th century, when the dangers

of global warming became of world wide political concern and the need to cut down the use of

fossil fuels in the future became apparent, the slow but steady triumph of hybrid automobiles

began with the Toyota Prius, which was presented in 1997.

4 Direction of Technological Change

Even though the direction of technological change is not the primary interest of this paper, it

is interesting to compare the results in this paper with those of the base model for directed

technological change in Acemoglu (2002, 2007). Acemoglu defines technical change as being

biased towards a certain input if it increases the relative marginal product of that particular

factor compared to other inputs. For the production technology used in this paper, technological

progress that is relatively biased towards input Q can be expressed as

∂x(A,Q,Z)/∂Q∂x(A,Q,Z)/∂Z

∂A> 0. (32)

Acemoglu (2002) finds that an increase in the supply of one input always leads to technical

change that is biased towards this input.

19

In this model, the direction of technical change is determined by fundamental researchers,

that choose the share coefficient ψ of the intermediate goods production function according to

economy’s expected relative supply of primary factors Q2t

Z2t. As the solution to the maximization

problem in (25), the optimal ψ∗ is given by

ψ∗ =Q2t

Q2t + Z2t

, (33)

hence ψ∗ rises if the expected relative endowment Q2t

Z2tincreases and vice versa.

The relative marginal product of Q compared to Z in intermediate goods production is given

by

∂x(Q,Z)/∂Q

∂x(Q,Z)/∂Z=

(ψ

1− ψ

) 1ε

·(Q

Z

) 1ε

, (34)

hence it increases in ψ. Both results, together with the fact that a change in ψ always comes

together with an increase in A, imply that technical progress is always biased towards the input

that has become relatively more abundant, which is in line with Acemoglu (2002, 2007).

Notice however, that this finding is only true with respect to technological progress that results

from fundamental innovations. In this paper, technological progress in the short run can result

from fundamental innovations as well as from secondary development. A change in the relative

factor supply will only result in directed technical progress, if a fundamental innovation is made.

If, on the other hand, fundamental researchers are unsuccessful and technological progress results

only from secondary development, only factor neutral technical change will be observed.

5 Simulation

To illustrate the quantitative significance of the model’s implications, I simulate the model

and study the effect of the relative changes in fossil fuel prices compared to renewable energy

sources in the US from 1870 until today. Figures 4 and 5 display the development of fossil fuels

(excluding nuclear energy) and renewable energy for primary energy consumption and the first

purchase price for crude oil over time in the US.13 It can be seen that the share of fossil fuels

and renewables has remained fairly constant over the past 60 years with a slight shift towards

renewables between the second half of the 1970s until the beginning of the 1980s and from 2005

onward. Similarly, the price for crude oil has been relatively stable with the exception of the

time between 1910–1920, the two energy crises in the 1970s during which the real price increased

dramatically, and a gradual increase from 2000 onward.

For the simulation, the period length is set to 10 years and the model’s parameters are set to

match the long term development of the US economy characterized in the spectral analysis by

Korotayev and Tsirel (2010), which covers the time from 1871–2007. The authors estimate an

average long-term cycle length of 50 years and an annual growth rate of 2.8%. Accordingly, the

13The price for crude oil is used as a proxy for fossil fuel prices in the simulation.

20

1950 1960 1970 1980 1990 2000 20100%

20%

40%

60%

80%

100%

Fossil FuelsRenewables

Figure 4: US primary energy consumption by source (Source: EIA)

1870 1890 1910 1930 1950 1970 1990 2010

0

20

40

60

80

100

US

Dol

lar

Nominal

Real (2010$)

Figure 5: US crude oil first purchase price (Dollar per barrel) (Source: EIA)

productivity increase of a fundamental innovation is set to γ = 3.14 The monopolist’s share

of the productivity gain of a new innovation ρ and the individual probability to be successful

in fundamental research p have a very similar effect in the calibration, therefore one of them

has to be held constant while the other is adjusted to yield the estimated growth rate. I set

p = 0.5 and ρ = 0.81. The average annual growth rate during the upswing phase is estimated

between 3.35–3.66 whereas for the downswing phase it is between 1.68–1.95. To match these

values, I set the parameters for secondary development to µ = 1.30 and φ = 0.75. The elasticity

of substitution between inputs is taken from Lanzi and Sue Wing (2011), who estimate a value

of ε = 1.46 for fossils fuels and renewables in the US energy sector. For the expectations about

the future factor supply, I assume that the agents expect the supply to remain at its current

level, so E1t

(Q2t

)= Q1t and equally so for Z.15

The simulation covers the period for which information on crude oil prices are available, that is

from 1870 onward. Five additional periods are simulated upfront and then cut off to avoid the

14This value is also used in Acemoglu and Cao (2010) for a fundamental innovation, based on the findings inScherer (1986) and Freeman and Soete (1997).

15Since energy price hikes have typically arrived in the form of unforeseeable shocks during the 20. century,this assumption seems to be justified. Only lately, from the middle of the 1990s onward, a gradual increase ofenergy price can be noted, which should induce agents to adapt their expectations accordingly. Nevertheless, forthe objective of this simulation, to illustrate the model’s implications in terms of renewed fundamental research,the correct assumption for the agents’ expectations about future energy prices has no great relevance. Even ifthe agents had perfect foresight, the reaction in terms of increased fundamental research would be similar, onlythe timing would vary.

21

influence of initial conditions; especially the fact that there is zero secondary development at the

beginning of the simulation and hence the amount of fundamental research is at the maximum.

For the presented results, the development of the economy has been simulated 1,000 times and

the mean of the outcomes is reported. To eliminate the influence of extreme outcomes, the

lowest and highest 10% of outcomes in terms of productivity at the end of the simulation period

are dropped. I do the complete simulation in two versions: one without changes in the supply

of crude oil, which serves as a benchmark, and one where the price changes given in Figure 5

are taken into account. To be in line with the model, these price changes have been translated

into changes in the (inelastic) supply of crude oil while the supply of renewables has been held

constant.

Figure 6 displays the development of the simulated economy without crude oil price changes

taken into consideration.16 The upper part shows the share of fundamental researchers and

the lower part gives the annual rate of productivity growth. It turns out, that the share of

fundamental researchers falls over time until it becomes zero at the end of the simulation period.

Accordingly, productivity growth diminishes constantly over time with only minor fluctuations.

1870 1890 1910 1930 1950 1970 1990 2010

0

0.1

0.2

0.3 Fundamental Research

1870 1890 1910 1930 1950 1970 1990 2010

1%

2%

3%Productivity Growth

Figure 6: Simulation without price changes

By contrast, Figure 7 depicts the simulation results when the changes in the crude oil price

are included in the simulation.17 It turns out that in this case, fundamental research and

productivity growth do not decline over time and that they follow the changes in the supply of

16To provide smooth curves, annual numbers are interpolated from the 10-year-period raw data.17To take the length of a simulation period into account, 10-year rolling averages of crude oil prices have been

used.

22

crude oil given in Figure 5. After some initial fluctuations, the crude oil price remains fairly

constant until 1910. Accordingly, the share of fundamental researchers and productivity growth

declines in the simulation. From 1910 onward, the crude oil price starts to increase substantially

and more than doubles around 1920 compared to average value of the previous period. In the

simulation, these price changes nearly double the share of fundamental researchers in 1920

compared to 1910 which leads to increased productivity growth. After the peak, the crude oil

price becomes fairly stable again. The next price hike takes place around 1950 which is mirrored

in the simulation by a reinforcement of fundamental research and a higher productivity growth

rate. This is followed by the double oil crisis during the 1970s, which again is reflected in the

simulation by a higher share of fundamental research; the same is true for the price increase

from 2000 onward.

1870 1890 1910 1930 1950 1970 1990 2010

0

0.2

0.4

0.6

Fundamental Research

1870 1890 1910 1930 1950 1970 1990 2010

1%

2%

3%

4%

Productivity Growth

Figure 7: Simulation with changes in crude oil price

The simulations show that real world factor price changes have a strong influence on the in-

centives for fundamental research. While fundamental research eventually ceases over time

and path dependence lets the simulated economy become trapped in a technological lock-in

in the case with no price changes, the version that took the changes in crude oil prices into

account could avoid this fate. Although fundamental research declined during the phases with

stable prices, the substantial changes in the oil price that occurred several times during the

simulation period stimulated fundamental research and led to new fundamental innovations, so

that neither research nor productivity growth ceased in the long run. These results indicate

that the model’s implications are quantitatively important and significantly influence real world

economic development.

23

6 Conclusions

Path dependence denotes the fact that the trajectory of technological development is shaped

by previous decisions and outcomes which can lead to the dominance of certain technologies in

spite of the availability of better alternatives. However, this dominance is sometimes overcome

when changes in the environment induce new innovations and make alternative technologies

more attractive.

In this paper, I develop a model that captures the origins of path dependence and also intro-

duces a mechanism of induced innovation which allows to escape from technological lock-in.

Due to imperfect spillovers of secondary development, new technologies can be inferior in com-

parison to dominant existing technologies and the economy becomes trapped in a technological

lock-in. However, since fundamental innovations can be directed to favor a particular input

factor, changes in the relative supply of primary factors increase the productivity gain of a new

technology and induce research to overcome the lock-in.

The model is able to explain the long waves of economic development, where supply changes

trigger a new growth cycle. A simulation of the model using the changes of crude oil prices

indicates, that the model’s implications are quantitatively relevant. With its main finding,

that changes in the supply of primary factors can induce innovative activity and stimulate

technological progress, the paper also provides a new rationale for policies that aim to increase

social welfare and reduce environmental damage by the use of Pigouvian taxes or pollution

permits.

For future work, the model could be extended in a number of ways. First, the assumption of zero

spillovers of secondary development between fundamental technologies could be relaxed to allow

partial spillovers as in Redding (2002). Obviously, some of the human capital and efficiency

improvements can be also used for other technologies as well. For the keyboard layout example,

it is documented that QWERTY-trained typists need less time to adapt to the Dvorak layout

than untrained people. Also the development of alternative-drive vehicles benefits from many

of the improvements of gasoline cars over the last century. Second, the adjustment to a new

relative supply regime, which is done within one fundamental innovation, could be limited in

such a way that it takes a number of fundamental innovations until the economy has completely

adapted to the new environment. This would move the model closer to the typical models of

directed technological change, where these adjustments take place gradually. Third, the model

could be easily extended to use a larger number of primary factors. With a nested intermediate

goods production function, different elasticities of substitution can be taken into account. A

change in the supply of any of these factors could than induce new research. Such an extension

could be especially helpful for empirical work.

24

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